In nanoimprint lithography, a mold or template having a surface with a nanopattern is used to imprint the nanopattern onto a surface of a nanoimprint object, e.g., a glass or polymer substrate. Typically, a substrate or wafer is held on a solid rigid flat surface of a vacuum chuck and a template is moved to essentially stamp the surface of the substrate. Many systems employ flexible molds and can be employed on rollers or can be attached to relatively complex actuation systems that can independently stamp sections of the flexible mold onto the surface of the substrate, e.g., from right to left. However, existing methods suffer from a number of issues, particularly for relatively thin, flexible substrates. For example, the substrate can be deformed in a non-uniform or uncontrolled manner as it is held against its vacuum chuck, and such deformations can lead to intense stresses and strains being present in the substrate during the imprint process. When the substrate is eventually released from the vacuum chuck, errors in the imprinted pattern can occur as the stresses release. In addition, when flexible molds are employed, the required bending of the mold itself can lead to imprint errors. Therefore, there is a need in the art to provide an improved method for nanoimprint lithography.